Please help me convert equation to matlab code.

Question

N K 2012-2-15

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编辑： Greg Heath 2013-10-13

Deal all.

I need you help to convert this equation to matlab code to plot DCT basis function graph.

Equation is in

http://www.ece.ucsb.edu/courses/ECE158/158_F10Gibson/158LAB6.pdf

at equation (1) and (2).

*I'm not a student in this class but I need DCT concept to write code.

I spend a lot of time to write it but it doesn't work.

Please help me. I must have DCT basis function for my work.

Best regard.

ps. If you have DCT basis function, please share it to me.

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Answer 1

Matt Tearle 2012-2-15

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在 MATLAB Online 中打开

Assuming that x is a column vector

N = length(x);
k = 0:(N-1);
DCTbasis = cos(k'*(2*k+1)*pi/(2*N));
w = sqrt(2/N)*DCTbasis*x;
w(1) = w(1)/sqrt(2);

will do the job. If you have Signal Processing Toolbox, so will

w = dct(x);

:)

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N K 2012-2-15

Thanks for you answer.

So if I want to plot dct basis function graph follow this picture.

(DCT 8 point)

http://instruct1.cit.cornell.edu/courses/ee476/Math/DCTIIbasis8.png

could you tell me how to do that (I'm novice in matlab).

best.

Matt Tearle 2012-2-15

I'm not sure what you're trying to achieve with your follow-up question. It looks a lot like Q 1.1 in the lab, but you already found a nice visualization. I don't see what recreating the visualization in MATLAB will gain you -- it's messy because the visualization is plotting the underlying continuous function, not just the 8 sample points. If you run the code I gave, with x being any 8-by-1 vector, then the rows of the DCTbasis matrix will be the values of the basis functions, at the sample locations.

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